A gas is compressed adiabatically, which one of the follwing statement is NOT true.
- The change in the internal energy is equal to the work done on the gas
- The temperature of the gas increases
- There is no heat supplied to the system
- There is no change in the internal energy
The Correct Option is D
Solution and Explanation
Step 1: Understanding the adiabatic process.
In an adiabatic process, there is no heat exchange between the system and its surroundings, i.e., \( \Delta Q = 0 \). According to the first law of thermodynamics: \[ \Delta Q = \Delta U + W \] Where \( \Delta U \) is the change in internal energy, and \( W \) is the work done by the system. Since there is no heat exchange in an adiabatic process, we have: \[ 0 = \Delta U + W \quad \Rightarrow \quad \Delta U = -W \] This means that the change in the internal energy is equal to the negative of the work done by the system.
Step 2: Conclusion.
Thus, the internal energy of the gas changes during adiabatic compression. Therefore, the statement "There is no change in the internal energy" is incorrect.
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